Here's my guess on what happened.
Eze was set on Woolwich earlier in the window, but things did not move forward (maybe Woolwich too was waiting for the release clause to expire to get a better deal).
It looked like Woolwich was not going to pursue the player, so we expressed interest, which was welcomed by Palace and the player. Was this because they wanted to jolt Woolwich into coming back in for him, or was it because they genuinely thought this was the best deal for them? We have no idea (and this is the key point - no one really knows and you can make assumptions all you want).
Woolwich does end up bidding for the player and, since Eze's heart was set on them, naturally the deal with Woolwich happens.
Should we have not tried to sign him just because there was an earlier link with Woolwich? If we didn't everyone would be moaning that we are not trying. We tried and got gazzumped because Eze wanted Woolwich and everyone is moaning that it was foolish to try. In retrospect, yes it was. But at the time we had a clear path to sign the player. This is not the first time that this happens in transfers. We've done it to other teams ourselves.
That's all there is to it. Blame whomever you want, but this is not unusual. People are just getting more worked up about it because of the MGW fiasco earlier in the window.